Given the equation 5y - 3x = 1, how can I find solution points where x
and y are both integers? Also, how can I show that there will always be
integer points (x,y) in ax + by = c if a, b and c are all integers?

I've read the FAQs and other questions sent to you concerning why
0.999... equals one, but I'm still not convinced. I don't entirely
understand infinity and think it creates more problems than it solves.

If (X,Y) is a point in the 1st quadrant on the unit circle and m is the
slope of the line passing through (X,Y) and the point (0,-1), how can I
express the coordinates (X,Y) in terms of m? Can this be used to generate
Pythagorean triples?

We say that f is linear provided that for every x, y in its domain,
f(x+y) = f(x) + f(y). Show that if f is linear and continuous on R (the
set of real numbers), then f is defined by f(x) = cx for some c belong to
R.